[R-sig-eco] Doing repeated measures on a randomized block design

[Pedro Pequeno]

Dear Richard,

your question could be handled using a linear model incorporating a
temporal autcorrelation structure within trees. However, I don't think
using "tree" as random factor (e.g. in lme()) would be very helpful here
because random factors assume a compound symmetry autocorrelation structure
(same correlation for any temporal distance), which is probably overly
simplistic for long time series. Instead, you could use Generalized Least
Squares, gls() in R, which is a standard choice in such cases. For instance:

gls(FvFm ~ Exposure, correlation = corAR1(form = ~time|Tree), data =
perm.fvfm)

This will fit a model assuming a first-order autoregressive correlation
structure, i.e. residual autocorrelation should decrease as the temporal
distance between them increases. Notice that "time" should be the temporal
order of observations within trees, so you will have to convert your "Date"
to this format first. For other correlation structures, relevant R
functions and examples similar to yours, see Zuur et al. (2009), "Mixed
effects models and extensions in ecology with R".

Best wishes,

Pedro

Em sex, 14 de jun de 2019 às 14:42, Richard Boyce <boycer using nku.edu> escreveu:

> I’m measuring chlorophyll fluorescence (FvFm), my measured variable, on N
> and S exposures (treatment variable) of 4 red cedar trees. Here’s what the
> beginning of the data file looks like:
>
> head(perm.fvfm).
>
>   Tree Exposure   Date  FvFm
> 1    1        S 13.Feb 0.775
> 2    1        N 13.Feb 0.795
> 3    2        S 13.Feb 0.737
> 4    2        N 13.Feb 0.759
> 5    3        S 13.Feb 0.615
> 6    3        N 13.Feb 0.712
>
> If I were just doing this one time, this would be a randomized block
> design, where trees were the blocks (random variable) and exposure was the
> treatment variable (fixed variable). Actually, since there are only two
> treatment levels, it would be a paired t-test.
>
> However, I’ve repeated this on many dates (18 so far this year). So this
> also requires a repeated-measures design, with trees as subjects.
>
> Repeated-measures, however, usually have time (date) as a within-subject
> variable and then some other treatment that is a between-subjects variable.
> I don’t have have a between-subjects variable, however, as all subjects
> (trees) get both levels of exposure and all levels of time (date).
>
> I’ve searched the web, but there is not a lot out there for this kind of
> design. It looks like lm, lme, lmer, and permuco in R might all work, but
> advice for how to set up the Error() or random variable designations are
> confusing and sometimes contradictory. Any advice would be much appreciated!
>
> Thanks,
> Rick Boyce
>
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